import matplotlib.pyplot as plt
import numpy as np

plt.figure(figsize=[12, 8])

scale = 1
plt_x = np.linspace(0, scale, int(np.floor(2 * scale * 100 + 1)))

# plt.scatter([0], np.exp([0]), 'r')
plt.plot(plt_x, np.ones_like(plt_x), 'r--')
plt.plot(plt_x, 1 - plt_x, label='1 - x')
plt.plot(plt_x, np.log(1 - plt_x), label='ln (1 - x)')
plt.plot(plt_x, np.log(plt_x), label='ln (x)')

plt.legend()

ax = plt.gca()
ax.spines['top'].set_color('none')
ax.spines['right'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.spines['bottom'].set_position(['data', 0])
ax.spines['left'].set_position(['data', 0])

plt.show()
